A car in a roller coaster moves along a track that consists of a sequence of ups

Question

A car in a roller coaster moves along a track that consists of a sequence of ups and downs. Let the x axis be parallel to the ground and the positive y axis point upward. In the time interval from t= 0 to t = 4 s, the trajectory of the car along a certain section of the track is given by where A is a positive dimensionless constant. Derive a general expression for the speed v of the car. Express your answer in meters per second in terms of A and t. The roller coaster is designed according to safety regulations that prohibit the speed of the car from exceeding Find the maximum value of A allowed by these regulations. Express your answer using two significant figures.

Explanation / Answer

find A. set the original equation = to 20m/s (your max velocity) and plug in your max time for t, 4s.

20= 4A+4^3A-6(4^2)
20= 68A-96
116=68A
116/68=A
1.7=A

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